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%I #18 Sep 08 2022 08:45:13
%S 1,8,42,186,766,3058,12062,47426,186606,735858,2909182,11528866,
%T 45781646,182104658,725311902,2891845506,11539011886,46070609458,
%U 184025468222,735329653346,2938999333326,11749034250258,46975237266142
%N Expansion of (1 - 2*x - 3*x^2 - 4*x^3)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)).
%C Second binomial transform of A093380.
%H Vincenzo Librandi, <a href="/A093381/b093381.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,50,-24).
%F a(n) = 4/3 - 5*2^n + 2*3^n + 8*4^n/3;
%F a(n) = 2*A000244(n) - 5*A000079(n) + 4*A001045(2n+1).
%F a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4), n > 3. - _Harvey P. Dale_, May 29 2013
%t CoefficientList[Series[(1-2x-3x^2-4x^3)/((1-x)(1-2x)(1-3x)(1-4x)),{x,0,30}],x] (* or *) LinearRecurrence[{10,-35,50,-24},{1,8,42,186},30] (* _Harvey P. Dale_, May 29 2013 *)
%o (Magma) [4/3-5*2^n+2*3^n+8*4^n/3: n in [0..30]]; // _Vincenzo Librandi_, May 31 2011
%Y Cf. A033484.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Apr 28 2004